@article{34670, author = {{Black, Tobias}}, issn = {{0218-2025}}, journal = {{Mathematical Models and Methods in Applied Sciences}}, keywords = {{Applied Mathematics, Modeling and Simulation}}, number = {{06}}, pages = {{1075--1117}}, publisher = {{World Scientific Pub Co Pte Lt}}, title = {{{Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties}}}, doi = {{10.1142/s0218202520400072}}, volume = {{30}}, year = {{2020}}, } @article{31376, author = {{Hoffmann, Max}}, journal = {{Der Mathematikunterricht}}, pages = {{36–47}}, title = {{{Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver Zugang zur hyperbolischen Geometrie.}}}, volume = {{66 (6)}}, year = {{2020}}, } @inbook{56244, author = {{Barzel, Bärbel and Biehler, Rolf}}, booktitle = {{Professional development and knowledge of mathematics teachers}}, pages = {{163–192}}, publisher = {{Routledge}}, title = {{{Theory-Based Design of Professional Development for Upper Secondary Teachers–Focusing on the Content-Specific Use of Digital Tools}}}, year = {{2020}}, } @article{16710, abstract = {{In this work we present a set-oriented path following method for the computation of relative global attractors of parameter-dependent dynamical systems. We start with an initial approximation of the relative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method. By using previously obtained approximations of the parameter-dependent relative global attractor we can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole subdivision procedure. We illustrate the feasibility of the set-oriented path following method by exploring the dynamics in low-dimensional models for shear flows during the transition to turbulence and of large-scale atmospheric regime changes . }}, author = {{Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}}, issn = {{1536-0040}}, journal = {{SIAM Journal on Applied Dynamical Systems}}, pages = {{705--723}}, title = {{{A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}}}, doi = {{10.1137/19m1247139}}, year = {{2020}}, } @inbook{35811, author = {{Biehler, Rolf and Durand-Guerrier, Viviane}}, booktitle = {{Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)}}, editor = {{Hausberger, T. and Bosch, M. and Chelloughi, F.}}, keywords = {{Number Theory, Algebra, Discrete Mathematics, Logic, Research in University Mathematics Edcuation}}, pages = {{283--287}}, publisher = {{University of Carthage and INDRUM}}, title = {{{University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic}}}, year = {{2020}}, } @inbook{35829, author = {{Kempen, Leander and Krämer, Sandra and Biehler, Rolf}}, booktitle = {{Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)}}, editor = {{Hausberger, T. and Bosch, M. and Chelloughi, F.}}, pages = {{358--367}}, publisher = {{University of Carthage and INDRUM}}, title = {{{Investigating high school graduates’ personal meaning of the notion of “mathematical proof”}}}, year = {{2020}}, } @article{33594, author = {{Rezat, Sebastian and Rezat, Sara}}, journal = {{Die Grundschulzeitschrift 320}}, pages = {{10--13}}, title = {{{Schulbücher. Werkzeuge zum Üben in den Fächern Deutsch und Mathematik}}}, volume = {{320}}, year = {{2020}}, } @inbook{35821, author = {{Budde, Lea and Frischemeier, Daniel and Biehler, Rolf and Fleischer, Franz Yannik and Gerstenberger, Dietrich and Podworny, Susanne and Schulte, Carsten}}, booktitle = {{New Skills in the Changing World of Statistics Education: Proceedings of the Roundtable conference of the International Association for Statistical Education (IASE), July 2020}}, editor = {{Arnold, P.}}, publisher = {{ISI/IASE}}, title = {{{Data Science Education in Secondary School: How to Develop Statistical Reasoning When Exploring Data Using CODAP}}}, year = {{2020}}, } @inbook{35913, author = {{Liebendörfer, Michael and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler, Rolf and Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}}, booktitle = {{Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)}}, editor = {{Hausberger, T. and Bosch, M. and Chelloughi, F.}}, publisher = {{University of Carthage and INDRUM}}, title = {{{The role of learning strategies for performance in mathematics courses for engineers}}}, year = {{2020}}, } @inbook{35912, author = {{Lankeit, Elisa and Biehler, Rolf}}, booktitle = {{Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)}}, editor = {{Hausberger, T. and Bosch, M. and Chelloughi, F.}}, publisher = {{University of Carthage and INDRUM}}, title = {{{“I only know the absolute value function”–About students’ concept images and example spaces concerning continuity and differentiability}}}, year = {{2020}}, } @article{34841, abstract = {{We give an exact formula for the number of G-extensions of local function fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application we give a lower bound for the corresponding counting problem by discriminant. }}, author = {{Klüners, Jürgen and Müller, Raphael}}, issn = {{0022-314X}}, journal = {{Journal of Number Theory}}, keywords = {{Algebra and Number Theory}}, pages = {{311--322}}, publisher = {{Elsevier BV}}, title = {{{The conductor density of local function fields with abelian Galois group}}}, doi = {{10.1016/j.jnt.2019.11.007}}, volume = {{212}}, year = {{2020}}, } @article{19945, abstract = {{Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is connected to conservation properties and other geometric features of solutions to the PDE and, therefore, of great interest for numerical integration. For the example of Burgers' equations and related PDEs we use Clebsch variables to lift the original system to a collective Hamiltonian system on a symplectic manifold whose structure is related to the original Lie-Poisson structure. On the collective Hamiltonian system a symplectic integrator can be applied. Our numerical examples show excellent conservation properties and indicate that the disadvantage of an increased phase-space dimension can be outweighed by the advantage of symplectic integration.}}, author = {{McLachlan, Robert I and Offen, Christian and Tapley, Benjamin K}}, issn = {{2158-2505}}, journal = {{Journal of Computational Dynamics}}, number = {{1}}, pages = {{111--130}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{Symplectic integration of PDEs using Clebsch variables}}}, doi = {{10.3934/jcd.2019005}}, volume = {{6}}, year = {{2019}}, } @article{21944, author = {{Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}}, issn = {{0021-9606}}, journal = {{The Journal of Chemical Physics}}, title = {{{Coarse-graining molecular systems by spectral matching}}}, doi = {{10.1063/1.5100131}}, year = {{2019}}, } @inbook{8577, author = {{Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard}}, booktitle = {{Beiträge zum Mathematikunterricht 2019}}, title = {{{Erklärung von Mathematikleistung im Ingenieursstudium}}}, year = {{2019}}, } @article{16709, author = {{Sahai, Tuhin and Ziessler, Adrian and Klus, Stefan and Dellnitz, Michael}}, issn = {{0924-090X}}, journal = {{Nonlinear Dynamics}}, title = {{{Continuous relaxations for the traveling salesman problem}}}, doi = {{10.1007/s11071-019-05092-5}}, year = {{2019}}, } @article{10593, abstract = {{We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. Using a recent convergence result for the numerical approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the value of the K-ROM based objective function converges in measure to the value of the full objective function. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier–Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy.}}, author = {{Peitz, Sebastian and Klus, Stefan}}, issn = {{0005-1098}}, journal = {{Automatica}}, pages = {{184--191}}, title = {{{Koopman operator-based model reduction for switched-system control of PDEs}}}, doi = {{10.1016/j.automatica.2019.05.016}}, volume = {{106}}, year = {{2019}}, } @article{10595, abstract = {{In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set.}}, author = {{Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}}, issn = {{0925-5001}}, journal = {{Journal of Global Optimization}}, number = {{4}}, pages = {{891--913}}, title = {{{On the hierarchical structure of Pareto critical sets}}}, doi = {{10.1007/s10898-019-00737-6}}, volume = {{73}}, year = {{2019}}, } @inproceedings{10597, abstract = {{In comparison to classical control approaches in the field of electrical drives like the field-oriented control (FOC), model predictive control (MPC) approaches are able to provide a higher control performance. This refers to shorter settling times, lower overshoots, and a better decoupling of control variables in case of multi-variable controls. However, this can only be achieved if the used prediction model covers the actual behavior of the plant sufficiently well. In case of model deviations, the performance utilizing MPC remains below its potential. This results in effects like increased current ripple or steady state setpoint deviations. In order to achieve a high control performance, it is therefore necessary to adapt the model to the real plant behavior. When using an online system identification, a less accurate model is sufficient for commissioning of the drive system. In this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system identification is proposed. The method does not require high-frequency signal injection, but uses the measured values already required for the FCS-MPC. An evaluation of the least squares-based identification on a laboratory test bench showed that the model accuracy and thus the control performance could be improved by an online update of the prediction models.}}, author = {{Hanke, Soren and Peitz, Sebastian and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}}, booktitle = {{2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)}}, isbn = {{9781538694145}}, title = {{{Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification}}}, doi = {{10.1109/precede.2019.8753313}}, year = {{2019}}, } @inproceedings{13106, author = {{Schumacher, Jan}}, booktitle = {{Beiträge zum Mathematikunterricht 2019}}, location = {{Regensburg}}, title = {{{Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen}}}, year = {{2019}}, } @inproceedings{13107, abstract = {{In this paper, we first outline a Hypothetical Learning Trajectory (HLT), which aims at a formal understanding of the rules for manipulating integers. The HLT is based on task formats, which promote algebraic thinking in terms of generalizing rules from the analysis of patterns and should be familiar to students from their mathematics education experiences in elementary school. Second, we analyze two students' actual learning process based on Peircean semiotics. The analysis shows that the actual learning process diverges from the hypothesized learning process in that the students do not relate the different levels of the diagrams in a way that allows them to extrapolate the rule for the subtraction of negative numbers. Based on this finding, we point out consequences for the design of the tasks.}}, author = {{Schumacher, Jan and Rezat, Sebastian}}, booktitle = {{Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)}}, editor = {{Jankvist, Uffe Thomas and Van den Heuvel-Panhuizen, Marja and Veldhuis, Michiel}}, keywords = {{diagrammatic reasoning, hypothetical learning trajectory, induction extrapolatory method, integers, negative numbers, permanence principle, semiotics}}, location = {{Utrecht}}, publisher = {{Freudenthal Group & Freudenthal Institute, Utrecht University and ERME}}, title = {{{A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers}}}, year = {{2019}}, }